
Exponential Transformations and Characteristics
Presentation
•
Mathematics
•
10th - 12th Grade
•
Hard
James Gonzalez
FREE Resource
14 Slides • 27 Questions
1
The Exponential Functions: Attributes and Transformations
2
The Basics
An exponential function with base b is defined by f(x)=abx where a ≠0, b > 0 , b ≠1, and x is any real number.
The base, b, is constant and the exponent, x, is a variable.
3
4
5
6
7
The Asymptote of Exponential Function
Asymptote - The line that the function approaches but never touches
The exponential function has a horizontal asymptote
For the function f(x) = 2x its asymptote is the x-axis or y=0
8
Multiple Choice
Which equation best describes the graph?
y = 2x + 4
y = 2x - 3
y = 2x - 4
y = 2x + 3
9
Multiple Choice
Find the domain.
all values less than 1
all real numbers
all positive numbers
all values less than 0
10
Multiple Choice
Determine the asymptote for the function
f(x)=3(2)x-4+5
x=4
y=4
x=5
y=5
11
Multiple Choice
What is the horizontal asymptote for the graph of
f(x)=-2(3)x+4-8 ?
y=8
y=-8
x=-8
x=-4
12
Multiple Choice
Asymptote?
y = 2
y = -2
x = 2
y = 0
13
Multiple Choice
What is the horizontal asymptote?
y = 2
y = -2
x = 2
y = 0
14
Multiple Choice
What is the horizontal asymptote?
y=3
y=-2
y=-3
(0,-3)
15
Multiple Choice
What is the range of the function shown below?
0 < y < 12
-2 < y < 5
y > 0
All Real Numbers
16
Multiple Choice
What is the domain of the function shown below?
-2 < x < 5
0 < x < 12
y > 0
All Real Numbers
17
Multiple Choice
What is the range of this graph?
y = 6
(0, -4)
y > -6
y < -6
18
Multiple Choice
What is the asymptote value in the function?
3
2
7
0
19
Multiple Choice
20
21
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27
Multiple Choice
What is the transformation?
Horizontal Translation left 2
Vertical Translation down 2
None
Reflection across the x-axis
28
Multiple Choice
Which of the following value translates the parent function down?
0
1
-1
-2
29
Multiple Choice
What is the transformation?
Vertical Translation up 2 and Horizontal translation right 1
Vertical Translation down 2 and Horizontal Translation left 1
Horizontal Translation left 2 and Vertical Translation up 1
Horizontal Translation right 2 and Vertical Translation down 1
30
Multiple Choice
What is the transformation?
Vertical Translation up 2
Vertical Translation down 2
Horizontal Translation left 2
Horizontal Translation right 2
31
Multiple Choice
What is the transformation?
Vertical Translation up 1
Vertical Translation down 1
Horizontal Translation left 1
Horizontal Translation right 1
32
Multiple Choice
Identify the y-intercept of the function −3(3)x+4
y-intercept at (0, -3)
y-intercept at (0, 1)
y-intercept at (0, -7)
33
Multiple Choice
Identify the asymptote of the function −3(3)x+4
y = -3
y = 1
y = 4
34
Multiple Choice
How has the function 7(3)x−5 been transformed from the parent function 7(3)x ?
Shifted up 5
Shifted down 5
Reflection over the x-axis
Reflection over the y-axis
35
Multiple Choice
What is the y-intercept of the function y=4(5)x?
(0, 0)
(0, 4)
(0, 5)
36
Multiple Choice
What is the asymptote of the function y=4(5)x?
y = 0
y = 4
y = 5
37
Multiple Choice
If f(x) is a transformation of g(x), describe the transformation.
g(x)=0.5x−3
f(x)=0.5x
Be careful! This is not the same question at #4!
Left 3 units
Right 3 units
Up 3 units
Down 3 units
38
Multiple Choice
If g(x) is a transformation of f(x), describe the transformation.
g(x)=0.5x−3
f(x)=0.5x
Left 3 units
Right 3 units
Up 3 units
Down 3 units
39
Multiple Choice
If g(x) is a transformation of f(x), describe the transformation.
g(x)=(−3)2x
f(x)=(3)2x
Down 3 units
Stretch vertically
Horizontal reflection
Vertical reflection
40
Multiple Choice
If g(x) is a transformation of f(x), describe the transformation.
f(x)=0.4x−1
g(x)=0.4x−2
Down 1 unit
Down 2 units
Up 1 unit
Up 2 units
41
Multiple Choice
If g(x) is a transformation of f(x), describe the transformation.
f(x)=2x g(x)=2x+4
Up 4 units
Down 4 units
Left 4 units
Right 4 units
The Exponential Functions: Attributes and Transformations
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